This invention relates generally to sigma-delta modulators and more particularly to sigma-delta modulators having compensation for analog circuit imperfections.
As is know in the art, one type of analog to digital converter (ADC) uses a sigma-delta modulator to convert an analog signal into a corresponding digital signal. Such modulator includes: a feedback loop filter fed by the input signal and the output signal produced by the modulator; and, a quantizer fed by the feedback loop filter to produce the modulator output signal. The feedback loop filter samples the analog signal at a rate (i.e., sampling frequency, f.sub.s) greater than the Nyquist sampling rate, to thereby oversample the analog signal, and the majority of any resulting quantization noise produced by the quantizer is shifted in frequency (i.e., shaped) to a band greater than the bandwidth of the analog signal. The ratio of the sampling frequency, or rate, f.sub.s, to the Nyquist rate is referred to as the oversampling ratio, OSR. The frequency spectrum of the output signal, v.sub.o, is shown in FIG. 1 to include, in the "in-band" portion of the frequency spectrum, the frequency components primarily associated with the analog signal, and in the "out-of-band" portion of the frequency spectrum, primarily the shaped quantization noise. The frequency shifted (i.e., shaped) quantization noise is then reduced by a digital filter fed by the modulator output which produces digital words representative of the analog input signal. The digital words are produced at an output frequency, f.sub.OUT, much less than the sampling rate, f.sub.s. A sigma-delta ADC 10 is shown in FIG. 1 to include: (1) a sigma-delta modulator 11, having a feedback loop filter 12, quantizer 14, a digital to analog converter (DAC) 16; and (2) a digital decimation filter 18.
A multi-stage (i.e., cascade) sigma-delta modulator ADC 20 is shown in FIG. 2A to include a modulator system 22 and the digital decimation filter 18. The modulator system 22 includes the sigma-delta modulator 11 described in FIG. 1, an analog to digital converter (ADC) 26, and a quantization noise canceler 28 fed by the sigma-delta modulator 11 and the ADC 26. As noted above in connection with FIG. 1, the output of the sigma-delta modulator 11 here has the "in-band" frequency components indicated in the low frequency portion of the spectrum. These components are primarily associated with the analog signal and the "out-of-band" frequency components are shown in the higher frequency portion of the spectrum and are primarily associated with the shaped quantization noise. For example, as shown in FIG. 2, the output signal, V.sub.o, produced by the sigma-delta modulator is a composite signal which may be represented as U+HQ, where U is the component of the output signal associated with the analog input signal, (i.e., includes the "in-band" frequency components of the output signal, V.sub.o), Q is the quantization noise, H is a function of the electrical characteristics of the modulator 11. More particularly, H is representative of the quantization noise transfer function shown in FIG. 1. It is noted in FIG. 1 that H is a high-pass filter rejecting the "in-band" quantization noise components. Thus, the shaped quantization noise component of the signal V.sub.o is represented as HQ. Thus, the output signal of the modulator 11 on line 35 may be represented as V.sub.o =U+HQ.
Referring to FIG. 2A, a signal is produced at the output of the feedback loop filter 12 (i.e., on line 30) having as a component thereof the quantization noise, Q; here representative of the difference between the un-filtered (i.e., pre-filtered) quantization noise, Q and the filtered quantization noise, HQ. That is, the signal on line 30, V'.sub.1, may be represented as U+Q(H-1). The signal on line 30 is digitized by the ADC 26 to thereby provide a digital signal V.sub.1 which represents an estimate of the quantization noise, Q; more particularly, U+Q(H-1).
The quantization noise canceler 28 includes: a subtractor 32 fed by the ADC 26 (i.e., Q(H-1)+U) and the modulator 11 output signal, V.sub.o =U+HQ, to produce an output signal which represents Q. The subtractor 32 output signal Q is fed to a digital filter 34. The transfer function of the digital filter 34 is an estimate, H', of the noise transfer function, H. The output of the digital filter 34 may be represented as H'Q, neglecting the effect of quantization error in ADC 26. The canceler 28 includes a second subtractor 36 fed by the output of the modulator 11, i.e., the signal V.sub.o =U+HQ, and the output of the digital filter 36, H'Q, to produce a signal on line 37 which may be represented as U+Q(H-H'). Thus, if the noise transfer function, H, of the sigma-delta modulator is known, i.e., H=H'), the signals V.sub.o and V.sub.1, are processed in the quantization noise canceler 28 to remove, i.e., cancel, the shaped quantization noise HQ from the composite signal V.sub.o. The noise transfer function, H, is related to the electrical characteristics of the modulator 11. The modulator 11 typically includes analog components, such as an analog integrator (i.e., operational amplifier and feedback capacitor) and switched, sampling capacitors in the feedback loop filter 12, the electrical characteristics of which vary with temperature. Further, the modulators are fabricated as integrated circuits and therefore the electrical characteristics vary from chip to chip because of processing variations. Thus, while an estimate of H (i.e., H') is provided as a digital filter 34 in the quantization noise canceler 28, such estimate, H', is typically representative of the actual noise transfer function, H, at a nominal operating temperature statistically averaged over a range of the chips. However, because the quantization noise canceler 28 merely stores an "average" digital representation of H (i.e., H') which will not change with temperature or processing conditions, variations in the modulator 11 electrical characteristics will result in an error in the removal, i.e., cancellation, of the shaped quantization noise component of the composite signal, V.sub.o. That is, a residual shaped quantization noise, Q(H-H'), will remain in the signal produced by the canceler 28 on line 37, where H is the actual noise transfer function and H' is the "average", estimated noise transfer function used by the digital cancellation filter.
Referring now to FIG. 2B, an alternative digital to analog converter 20a is shown. Here, modulation system 22a includes a quantization noise canceler 28a and an additional DAC 17 fed by the output of quantizer 14. The signal on line 30 and the output of DAC 17 are subtracted to produce a signal representative of the pre-filtered quantization noise, Q. The ADC 26 digitizes such signal to produce a digital signal representative of the pre-filter quantization noise, Q. Thus, the filter 34, which is fed by the ADC 26 produces an output signal H'Q, as in the system 22 of FIG. 2A. Thus, as in the system 22 in FIG, 2A, the signal produced at the output of the quantization noise canceler 28a may be represented as: U+Q(H-H'), where Q(H-H') represents any residual quantization noise resulting from errors in the estimate of H'.
Various techniques have been suggested to remove this residual error, Q(H-H'). Some of these techniques are reported in my papers entitled "On-Line Digital Compensation of Analog Circuit Imperfections for Cascaded .SIGMA..DELTA. Modulators" by A. Wiesbauer and G. C. Temes IEEE-CAS region 8 Workshop in Pavia, Sep. 13-14, 1996 and "Adaptive Digital Compensation of Analog Circuit Imperfections for Cascaded .SIGMA..DELTA. Modulators" by A. Wiesbauer and G. C. Temes, 30th Asilomar Conference on Signals, Systems, and Computer, Pacific Grove, Calif., Nov. 3-6, 1996, the entire subject matter of both papers being incorporated herein by reference.